Source recognition memory deficits have repeatedly been observed in people with schizophrenia (SZ), and have also recently been observed in their first-degree relatives. These deficits have been hypothesized to result, at least in part, from impairments in the conscious recollection process. Although other processes are clearly also affected in SZ, it has been proposed that impairments in the conscious recollection process could be a parsimonious explanation for the source memory deficits observed in their relatives. Here, we tested 25 patients with SZ and 34 of their non-affected parents, as well as two groups of matched healthy controls, on a short-term associative memory task that shares the characteristics of standard source recognition tasks but minimizes the need for recollection of stored information from memory. This task was administered in order to determine if deficits can still be observed in these people when involvement of the conscious recollection process is minimized. We observed deficits on our short-term source memory task in people with SZ, but their first-degree relatives did not share this deficit. These results support the idea that multiple memory processes supporting associative/source memory are affected in SZ, whereas the source memory deficits previously observed in relatives of SZ seem specific to tasks that rely on the conscious recollection process.